What makes a matriarch? Is a matriarch the oldest female in the family, or the wisest, simply the one who usurps the role? We often conflate age and wisdom in our society, possibly because no one ever feels quite "wise," but it seems safe to assume that age confers wisdom. I think my own mother would have resisted the role of matriarch; it would not have appealed to her sense of the ephemeral. Julia, Liz's mother, made a classic old-world matriarch, but probably just because she was Old World right down to the accent, the home-cooked Hungarian meals, and the house dress persona. We all try to shoehorn May into the role, but she also resists it. This leaves me or Liz. Or really it just leaves Liz, because I think she covets the role. Which is maybe what makes a matriarch.
The concept of the matriarch, the crone, the wise old woman is very appealing. I am too young for this role, of course, and don't have enough of a satellite system, so to speak-- no young 'uns, and not much of an extended family. (Which brings up the other question of how large your tribe needs to be before it requires a matriarch.) I'm not sure people would really view me this way either. I suspect I am headed more towards Crazy Old Lady than Wise Old Lady.
The matriarch is the unanswerable Mother, the person with the final say. This is the appeal-- that someone can say- stop. Someone can say- do. That someone actually has the final answer and the right to an expectation of obedience, or at least compliance. It is this expectation that confers the power of the Matriarch, and by extension the wisdom. This is a feedback loop that reinforces the power-- if I give you power over me, I need to justify that with a belief in your wisdom, which gives you power over me.